Accelerators

The JUNA experimental facility features 400-kV electrostatic acceleration and high-intensity ion beams of H⁺, He⁺, and He²⁺. In general, the 400-kV accelerator adopts a two-step acceleration and separation mode for JUNA experiments (see Fig. 1). The beams are extracted at a potential of 20–50 kV from a high-intensity electron cyclotron resonance (ECR) ion source and post-accelerated up to 400 keV/q via the acceleration tube.

Fig. 1Full-screen View

(Color online) Complete side view of the JUNA 400-kV accelerator and Run-1 detection terminal. JUNA 400-kV can now provide high-intensity H⁺, He⁺, and He²⁺ beams

A 2.45-GHz ECR ion source with a permanent magnet structure has been developed for JUNA to provide H⁺ and He⁺ beams of several emA for routine operation [34], with a maximum intensity of 10 emA. However, a 2.45-GHz ECR ion source is not capable of producing intense He²⁺ beams. Therefore, a 14.5-GHz permanent magnet high-charge-state ECR ion source was developed to provide He²⁺ beams [39].

Through the development of 2.45-GHz and 14.5-GHz ECR ion sources and high-current beam transmission technology, the JUNA accelerator is capable of delivering 10-emA H⁺, 10-emA He⁺, and 2-emA He²⁺ beams. Two solenoids are set in the low energy beam transport (LEBT) system to match the beam to the acceleration tube. Two groups of triple quadrupoles are placed after the tube to match beam transport and meet the requirements of individual experiments. The inhibition of beam impurities is achieved by two dipoles. One is on the 400-kV high-voltage platform (30°), and the other is on the ground potential (90°). The beam transmission efficiency is higher than 90%, and the long-term stability of the beam energy is better than 0.05%. To calibrate the energy of the accelerator and the stoichiometry of the target, a typical proton beam was used to scan the resonance yield curves in known reactions. The benchmark resonances for the calibration originated from results reported in previous direct measurements. A typical uncertainty is approximately 1.1 keV for $E_{\text{beam}}=474.0$ keV (see, for example, [40] for details). The condition of high beam intensity provides great advantages for JUNA in conducting research in the field of nuclear astrophysics.

Detectors and targets

JUNA developed a high-efficiency BGO array and ³He tube array for gamma and neutron detection, respectively. Using low-background materials, integrated detection and shielding systems with a multilayer structure were established. The BGO array consists of eight BGO crystals, with each individual block occupying approximately 45° in the Φ direction. The neutron detection array consists of 24 ³He-filled proportional counters embedded in a polyethylene matrix. A 7% borated polyethylene layer was wrapped around the detection array to shield against environmental neutrons. Moreover, a waveform identification method for neutron detection and a flash number screening program for gamma detection were developed to further suppress the experimental background. The background levels of the JUNA detection arrays have been tested and are listed in Table 2 [41-43].

A mA-level high-power target was developed via surface microchannel water cooling. Furthermore, using a high-purity substrate combined with ion implantation, surface plating, and filtered cathodic vacuum arc (FCVA) technologies, a high-purity isotope-enriched target was prepared, which can solve various surface-effect problems caused by high-current beams (for example, see [44-47] for details). Under strong irradiation conditions, the stability of such a target can be maintained without significant loss of thickness; hence, there is no need to frequently replace the target during long-term experiments. Combined with the advantage of high-intensity beams, data can be collected more effectively.

High-efficiency detector arrays and radiation resistant targets, along with a cold trap to minimize carbon build-up on the target surface, a ring electrode applied with a negative voltage to suppress secondary electrons, and several apertures, constitute the detection terminal of the JUNA platform, as shown in Fig. 2. Note that Fig. 2 provides a general impression of the detection terminal, considering that the detection terminals used in JUNA Run-1 experiments are similar. The setup details of each experiment can be found in specific published articles.

Fig. 2Full-screen View

(Color online) Schematic of the JUNA Run-1 detection terminal

Using the equipment described above, five groups of key astrophysical reactions were studied during JUNA Run-1. Some research results and highlights are presented in the following sections.

JUNA Run-1 experiment results and achievements

In the JUNA Run-1 campaign, ¹²C(α,γ)¹⁶O, ¹³C(α,n)¹⁶O, ¹⁸O(α,γ)²²Ne, ¹⁹F(p,γ)²⁰Ne, ¹⁹F(p,αγ)¹⁶O, ²⁵Mg(p,γ)²⁶Al, and other reactions were measured with a high-intensity beam and high-efficiency detectors. The basic parameters are listed in Table 3 [40, 43, 48-50]. The results and their impact on astrophysics are discussed below in detail.

2.3.2

¹³C(α,n)¹⁶O

The ¹³C(α,n)¹⁶O reaction was the first neutron source used in the stellar models proposed by Cameron and Greenstein in 1954. This reaction produces neutrons for the main s-process in AGB stars, which synthesize nearly one half of elements heavier than iron in the Universe [71, 72, 20]. It may also be activated in metal-poor stars to supply neutrons for intermediate neutron-capture process (i-process) nucleosynthesis [73-77]. Precise determination of the reaction cross section is needed at associated Gamow windows of approximately E_c.m. = 0.15–0.3 MeV and 0.2–0.54 MeV to accurately predict the neutron density and final isotopic abundances from stellar models. Limited by the cosmic background in laboratories on the Earth’s surface, direct measurement was ceased at energies above E_c.m. = 0.27 MeV, with an error bar of approximately 60%, for being unable to effectively constrain the crucial threshold state and provide a reliable extrapolation down to stellar energies.

A recent breakthrough in the direct measurement of this reaction was reported by the LUNA collaboration at E_c.m. = 0.23–0.30 MeV, that is, the upper range of the s-process Gamow window [78]. However, for the extrapolation of the S-factor to low energies, they had to rely on other measurements at higher energies, which revealed inconsistencies (see text in [43] for details). As a result, their recommended reaction rate has a large uncertainty, leading to sizeable variations in the predictions of several important isotopes such as ⁶⁰Fe and ²⁰⁵Pb in the AGB model.

In JUNA research, a direct measurement of the ¹³C(α,n)¹⁶O reaction cross section was conducted over the range of E_c.m. = 0.24–1.9 MeV at underground (CJPL) and above-ground (Sichuan University, SCU) laboratories, with the highest precision to date [43]. The underground experiment was performed at E_c.m. = 0.24–0.59 MeV using the most intense beam available in deep underground laboratories. The above-ground measurement was performed with the same detection setup in the range of E_c.m. = 0.75–1.9 MeV using the ⁴He⁺ beam at the 3-MV Tandetron at Sichuan University to resolve the discrepancies among previous direct measurements at higher energies. Furthermore, 2-mm-thick ¹³C enriched targets with a purity of 97% were used to avoid the source of systematic uncertainty incurred by target deterioration in traditional thin-target experiments. The thick targets were highly stable, and only two targets were used for the entire experiment. At Sichuan University, the same detection setup was used to minimize additional systematic uncertainties in both thick-target and thin-target measurements.

The measurement provides self-consistent calibration of neutron detector efficiency, covers almost the entire i-process Gamow window, in which the large uncertainty of previous experiments was reduced from 60% to 15%, and eliminates the large systematic uncertainty in extrapolation arising from the inconsistency of existing datasets. Finally, the JUNA research provides a more reliable reaction rate for the study of the s- and i-processes, as well as the first direct determination of the alpha strength for the near-threshold state. The S-factor and corresponding best fit are shown in Fig. 3, revealing the importance of obtaining self-consistent data within a wide energy range. Future stellar models based on the next generation of multi-dimensional hydrodynamics simulations will be more predictive owing to the more reliable reaction rates provided by JUNA research.

Fig. 3Full-screen View

(Color online) S-factor of the ¹³C(α,n)¹⁶O reaction. The best fit and corresponding uncertainty recommended by JUNA (with both JUNA and SCU data) are shown as green solid lines and a green shaded band, respectively. The S-factors were corrected with the screening potential U_e = 0.78 keV. The measurement provides self-consistent data in a wide energy range and greatly reduces the large uncertainties of previous experiments [43]. The temperatures in T₉ on the top correspond to the central energy of the Gamow window on the bottom

2.3.3

¹⁸O(α,γ)²²Ne

According to classical AGB theory, convection first occurs between the H and He shells, then the H-rich material enters the He shell, and ¹²C, the product of He burning, forms a “pocket” composed of ¹³C. The ¹³C(α,n)¹⁶O reaction is subsequently activated, which produces the main neutron flux for the s-process (see also the discussion on the ¹³C(α,n)¹⁶O reaction above). This reaction is the main neutron source of low- or medium-mass AGB stars. In more massive AGB stars, the temperature becomes higher, and the ²²Ne(α,n)²⁵Mg reaction is activated, which plays an essential role in the weak component of the s-process [71, 72, 20, 79, 80]. ²²Ne is mainly produced via the ¹⁴N(α,γ)¹⁸F(β⁺,ν)¹⁸O(α,γ)²²Ne chain. Therefore, the production of neutrons from the ²²Ne(α,n)²⁵Mg reaction relies heavily on the front ¹⁸O(α,γ)²²Ne reaction rate. In addition, the ¹⁸O(α,γ)²²Ne reaction also determines the abundance ratio of neon isotopes synthesized in AGB stars. Because ²¹Ne/²²Ne can be constrained from the analysis of the SiC grains of meteoritic stardust originating from AGB stars with high precision [81], the comparison between model predictions and observational constraints help reveal the mass of parent AGB stars. In the energy range of interest (T ∼ 0.1–0.3 GK), the ¹⁸O(α,γ)²²Ne resonances that dominate the reaction rate occur near Eα = 470 and 660 keV. However, the former is weak and thus cannot easily be directly investigated at above-ground laboratories. The most recent attempt at this was the first direct measurement of the total resonance strength of the 470-keV resonance by CASPAR [82]. However, only two previous experiments, ¹⁸O(⁶Li,d)²²Ne and ²⁰Ne(t,p)²²Ne, have used indirect transfer reactions to determine the resonance energy, 470 ± 18 keV and 495 ± 12 keV, respectively (see references and discussion in [40]). The lack of a reported precise resonance energies persistently introduces substantial uncertainties to the ¹⁸O(α,γ)²²Ne reaction rate.

JUNA determined the resonance energy to be Eα = 474.0 ± 1.1 keV (see Fig. 4) by scanning the yield curve via both direct measurement and with the highest precision for the first time. In the JUNA research, ¹⁸O-enriched gas was used to produce Ti¹⁸O_x (where x is the atomic ratio of oxygen to titanium) targets through FCVA technology. The degradation of the target was measured to be 6% after 94 Coulomb ⁴He²⁺ irradiation by monitoring the maximum yield of the 660-keV resonance.

Fig. 4Full-screen View

(Color online) Thick target yield curve of the 470-keV resonance in ¹⁸O(α,γ)²²Ne. The lateral error represents the energy uncertainty of beams, and the vertical error represents the yield uncertainty. The dashed green line is the fitting curve, the blue shadow represents the uncertainty of the fitting curve, and the dashed red line marks the position of resonance energy [40]

Via the above efforts, the precision of the ¹⁸O(α,γ)²²Ne reaction rates was improved by up to approximately 10 times. The new reaction rates have allowed us to provide more accurate and precise predictions of ²¹Ne/²²Ne abundances in the intershell of AGB stars, improving the possibility of probing the origin of stardust SiC grains of different sizes (see Fig. 5)[40].

Fig. 5Full-screen View

(Color online) Ne isotopic ratios predicted in the intershell of different AGB models (filled symbols) using the JUNA ¹⁸O(α,γ)²²Ne reaction rates and those observed in meteoritic stardust SiC grains of different sizes [81] (open symbols). The symbol legend is shown at the top-left of the plot. The three regression lines denote fits to the KJB, KJC, and KJD samples, representing the mixing between a material of normal composition (≈solar, located at the top-right outside the plot boundaries) and AGB He-shell composition (located at the bottom left). The bottom-right inset shows the ²¹Ne/²²Ne ratios calculated with different ¹⁸O(α,γ)²²Ne reaction rates. See [40] for further details

2.3.4

¹⁹F(p,αγ)¹⁶O & ¹⁹F(p,γ)²⁰Ne

Fluorine nucleosynthesis is an open issue in modern astrophysics. In 1988, shortly after the discovery of SN1987, Woosley & Haxton [83] proposed fluorine production in Type II core-collapse supernovae (SNe) via neutrino spallation on ²⁰Ne nuclei. However, no fluorine spectrum has been observed in supernova remnants. In 1992, Jorissen et al. [84] observed HF lines from stars outside the solar system for the first time, providing evidence of fluorine production during shell-He burning in AGB stars. However, the observed fluorine abundance was considerably higher than the standard AGB model prediction, and additional mixing was still required [85]. This is the so-called fluorine overabundance problem. Although several other possible production sites were also investigated [86, 87], it remains unclear how each contributes to the observed fluorine abundance.

Precise ¹⁹F(p,α)¹⁶O reaction rates may play an essential role in solving this problem because fluorine and H are consumed at the same time and fluorine surface abundances may be modified [85, 88-91]. At the current temperature region of astrophysical interest (0.1–0.3 GK), the corresponding Gamow window is located at E_c.m. ≈ 70–350 keV. In this energy region, the ¹⁹F(p,α)¹⁶O reaction is dominated by the (p,α₀) and (p,αγ) channel. Previously, the (p,αγ) channel was measured down to E_c.m. ≈ 189 keV at an above-ground laboratory [92], which is still far from the lower edge of the Gamow window.

JUNA measured the ¹⁹F(p,αγ)¹⁶O channel down to the lowest energy of E_c.m. ≈ 72 keV [48, 93], and the energy region under investigation fully covered the Gamow window of AGB stars relevant to fluorine production. The ¹⁹F implanted targets [46, 47] exhibited a material loss of less than 7% under ∼ 200 C bombardment. Our new JUNA rate deviates significantly from the previous expectations [94] by a factor of 0.2–1.3 [48]. Together with the previous (p,α₀) data, the JUNA research provides strong experimental evidence that the total ¹⁹F(p,α)¹⁶O rate is dominated by the (p,α₀) channel at the low temperature region of 0.03–0.12 GK. Therefore, precise direct (p,α₀) measurement is required in the future.

In addition, as a breakout reaction from the CNO cycle, the ¹⁹F(p,γ)²⁰Ne reaction competes with ¹⁹F(p,α)¹⁶O and affects the (p,γ)/(p,α) rate ratio (see Fig. 6(a)). Previously, this reaction was thought to be weak compared to the ¹⁹F(p,α)¹⁶O reaction; therefore, most of the ¹⁹F produced by the CNO cycle would be recycled back into ¹⁶O, with no substantial changes in chemical abundance. JUNA measured the ¹⁹F(p,γ)²⁰Ne reaction down to a low energy point of 186 keV, reporting a key resonance at 225 keV [49]. This surprising resonance highlighted the origin of the anomalous calcium abundance observed in SMSS0313-6708, one of the oldest known stars (an ultra-metal-poor star), as suggested by a mechanism proposed to explain the chemical abundances measured in this early star. In this mechanism, after light metals such as carbon and oxygen are created, and early in the star’s evolution, subsequent follow-up proton and/or neutron-capture reactions generate an abundance of heavier elements up to calcium. Based on the JUNA results, the ¹⁹F(p,γ)²⁰Ne reaction rate of population III stars could be 7.4 times higher than previous estimates. Therefore, the JUNA results may explain the high calcium content of SMSS0313-6708 (see Fig. 6 (b)), which represents a significant achievement in interpreting astrophysical puzzles from the perspective of nuclear physics.

Fig. 6Full-screen View

(Color online) Calcium abundance predicted for SMSS0313-6708 based on different datasets (left panel) and CNO cycles (right-panel)[49]

2.3.5

²⁵Mg(p,γ)²⁶Al

The HEAO-3 satellite was the first to observe 1809-keV γ-rays emitted by ²⁶Al β decay [95, 96], marking the advent of the era of γ-ray astronomy. Subsequently, considerable efforts in γ-ray astronomy (for example, see Refs. [97-99]) have revealed the mass and distributions of ²⁶Al in the Galaxy. This discovery revealed that ²⁶Al nucleosynthesis is still active in our Galaxy because the half-life of the ²⁶Al g.s. is only 0.72 million years, which is significantly shorter than the age of our Galaxy.

The ²⁵Mg(p,γ)²⁶Al reaction is the primary pathway to producing ²⁶Al in several candidate astrophysical sites (for example, AGB stars [100], Wolf–Rayet stars [101], O-Ne-Mg nova [102], and core-collapse supernovae [103]), and its reaction rates are dominated by the resonant capture reactions of several low-energy resonances in the range of E_c.m. = 30–400 keV (at astrophysical temperatures below 0.2 GK). Many experiments have been performed since 1970; however, direct measurements in above-ground laboratories can only reach a resonance of 189 keV. In 2012, LUNA measured the resonance strength of ²⁵Mg(p,γ)²⁶Al at 92 keV in pioneering work [104, 105]. However, their results produced significant uncertainties for both the resonance strength and ground-state feeding factor owing to the relatively low beam intensity.

In JUNA research, the low-energy E_c.m. = 92, 130, and 189-keV resonances of the ²⁵Mg(p,γ)²⁶Al reaction were directly measured using a proton beam up to 2 emA, with the thicknesses of the ²⁵Mg isotopic targets set to approximately 60 μg/cm². The resonance strength ωγ and ground-state feeding factor were determined to be (3.8 ± 0.3) × 10^-10 eV and 0.66 ± 0.04, respectively. The JUNA results significantly reduced the uncertainties of the reaction rates at temperatures of 0.05–0.15 GK (see Fig. 7) and provided the ground-state feeding factor to the highest precision, that is, 0.66 ± 0.04, with at least a factor of 2 in uncertainty reduction when compared to the 12–33% relative uncertainty in previous studies (see text in [50]) for details. The recommended new ²⁵Mg(p,γ)²⁶Al reaction rates are a factor of 2.4 larger than those adopted in the REACLIB database at a temperature of around 0.1 GK. The new results indicate higher production rates for the ²⁶Al g.s. as well as cosmic 1.809-MeV γ-rays. The precise reaction rates from this research will provide an effective constraint for the study of the convection model in AGB stars and offer further support to explain the observed distribution of magnesium isotopes and the overall Mg–Al trend in stars such as M13 and NGC 6752.

Fig. 7Full-screen View

(Color online) Comparison between the JUNA ²⁵Mg(p,γ)²⁶Al reaction rates [50], the LUNA results(yellow-dashed line) [105], and those adopted in REACLIB (blue dotted line). The red shaded, yellow backslash, and dark violet areas represent the 1σ uncertainties of the present and other research

Indirect measurement of the ¹²C(α,γ)¹⁶O reaction with the ANC method

The cross section of the ¹²C(α,γ)¹⁶O reaction is extremely small in the Gamow window, which makes direct measurements difficult in ground-based laboratories. Indirect methods can determine the level parameters and achieve reliable extrapolations of the cross section from higher energies to the Gamow window through the phenomenological R matrix method [3]. The two main capture modes in the ¹²C(α,γ)¹⁶O reaction are the E1 and E2 g.s. transitions. The E2 transition to the g.s. mainly includes external capture to the ¹⁶O g.s. and the subthreshold 2⁺ resonance at Ex = 6.917 MeV. The E1 transition to the g.s. includes the low-energy tail of the broad 1^- resonance at Ex = 9.585 MeV and the subthreshold 1^- resonance at Ex = 7.117 MeV. The measurement of these two subthreshold states of ¹⁶O is the focus of indirect experiments.

The α-cluster transfer reaction is an important indirect method of studying the holy grail reaction [2]. Owing to its spin and isospin symmetry, and hence its high binding energy, an α-cluster can propagate within a nucleus relatively unperturbed for a significant amount of time [115]. α-clusters can preferentially populate natural-parity isoscalar states. By measuring the angular distributions of the α-cluster transfer induced by light nuclei, astrophysical reaction cross sections can be studied at higher energies than the Gamow window.

We performed a series measurements of ¹²C(¹¹B, ⁷Li)¹⁶O reactions to determine the ANCs and S factors of the ¹²C(α, γ)¹⁶O reaction. The experiments were conducted at the HI-13 tandem accelerator national laboratory of the CIAE [116-118]. The setup of the experiments is shown in Fig. 11 (an introduction to the Q3D spectrometer can be found in [119]). A 50-MeV ¹¹B beam was directed onto a natural carbon self-supported target to measure the angular distribution of the ¹²C(¹¹B,⁷Li)¹⁶O reaction. The reaction products were separated and detected by the a Q3D magnetic spectrometer, and a two-dimensional position-sensitive silicon detector recorded the position and energy information of the emitted particles. Fig. 12 shows the typical focal-plane position spectrum of ⁷Li at θ = 10° from the ¹²C(¹¹B,⁷Li)¹⁶O_g.s. reaction. The events in different reactions were clustered in different horizontal lines owing to having the same magnetic rigidity and different energies.

Fig. 11Full-screen View

(Color online) Setup used for the ¹²C(¹¹B, ⁷Li)¹⁶O experiments

Fig. 12Full-screen View

Focal-plane position spectrum of ⁷Li at θ = 10° from the ¹²C(¹¹B,⁷Li)¹⁶O_g.s. reaction[117]

The angular distribution of the ¹¹B+¹²C elastic scattering reaction was measured at the beginning and end of each angle to monitor the change in the target thickness and derive the optical potential of the entrance channel. We also measured the ⁷Li+¹⁶O elastic scattering reaction at an energy of 26 MeV to derive the optical potential of the exit channel.

Finite-range distorted-wave Born approximation (FRDWBA) calculations were performed to derive the ANCs of the ground, 6.917– MeV 2⁺, and 7.117– MeV 1^- states using the FRESCO code [120]. The parameters required in the FRDWBA calculations were the optical potentials of the entrance channel (¹¹B + ¹²C), exit channel (⁷Li + ¹⁶O), and core-core channel (⁷Li + ¹²C), and the binding potential parameters of ¹⁶O and ¹¹B. The parameters of the entrance and exit channels were calculated using a single-folding model [121, 122]. Hartree–Fock calculations with the SkX interaction [123] were used to obtain the nucleon density distributions of ¹¹B, ¹²C, and ¹⁶O. The nucleon density distribution of ⁷Li was taken from an independent particle model [124]. These density distributions were folded using the systematic nucleon-nucleus potential of the JLMB model [125]. The depths of these single-folding potentials were adjusted by normalizing the parameters to provide an optimum reproduction of the experimental data with the optical model. The uncertainties in the normalized parameters of the single-folding potentials of the entrance and exit channels were evaluated based on a least-squares minimization procedure. To obtain the SF and ANC of the α-cluster in ¹⁶O, the spectroscopic amplitudes of the α-cluster in the g.s. of ¹¹B were required. $S_{{}^{\text{11}}{\text{B,3S}}_{\text{0}}}$ and $S_{{}^{\text{11}}{\text{B,2D}}_{\text{2}}}$, taken from a former measurement of ⁷Li(⁶Li, d)¹¹B [126], are the single-particle wave functions describing the relative motion between an α-cluster and the ⁷Li core in the ¹¹B g.s. for quantum numbers NLj = 3S₀ and 2D₂, respectively.

Next, we present the first determination of the g.s. ANC of ¹⁶O using the ¹²C(¹¹B,⁷Li)¹⁶O transfer reaction. With the new g.s. ANC values, we performed R-matrix calculations to illustrate the impact of external capture on the uncertainty of the ¹²C(α, γ)¹⁶O reaction. We obtained the astrophysical S_E1 (300) and S_E2 (300) factors of the g.s. transitions to be 55.3 ± 9.0 keV b and 46.2 ± 7.7 keV b, respectively. The GS S_E2 (300) factor was obtained as 70 ± 7 keV b, resulting in an increase in the total S-factor from 140 to 162 keV b.

We also calculated the ¹²C(¹¹B,⁷Li)¹⁶O reaction rates. Our reaction rate was approximately 20% larger than deBoer’s value [3]. Following the calculation of Farmer et al. [53, 54], we calculated the BH masses. The calculated BH masses as a function of the initial He-core mass are shown in Fig. 13 [127-130]. The present reaction rate decreased the lower and upper edges of the BH mass gap by approximately 12% and 5%, respectively.

Fig. 13Full-screen View

(Color online) Black hole (BH) masses as a function of the initial helium-core mass with respect to the updated ¹²C(¹¹B,⁷Li)¹⁶O reaction rate [127]. The blue dots connected by a line in the left panel represent the results obtained using the rates from [128, 129], and the green dots connected by a line represent the results obtained using the new CIAE rates. The boundaries of their BH mass gap are represented by the blue dashed-dotted lines and green dotted lines, respectively. The right panel shows the masses of the BH from the first, second, and third Gravitational-Wave Transient Catalogs (GWTC1, GWTC2, and GWTC3), which restrict the median estimated mass of the primary to, with 90% confidence intervals [130]

Indirect measurement using the surrogate ratio method

Both nuclear reactors on the Earth and massive stars in the Universe contain abundant unstable nuclei with half-lives of several days to millions of years combined in their fuels. Neutron radiative capture reactions of such radionuclides play an important role in energy generation and nucleosynthesis [131, 132]. To date, the cosmic origin of elements heavier than iron is believed to be slow and rapid neutron-capture processes, and many (n,γ) reactions of radionuclides are intensely involved in the relevant reaction networks. The competition between the β-decay and neutron capture of these unstable nuclei decides the nucleosynthesis path and changes the abundances of the follow-up nucleus. Furthermore, the abundances of the unstable nuclei’s neutron-capture products are related to the neutron densities in massive stars, and the products of the unstable nuclei may be an effective probe to study the neutron density and related temperature inside. However, the (n,γ) cross sections are difficult to measure directly owing to the challenge in preparing the target materials of short-lived radionuclides. Therefore, several indirect methods have been proposed, and many experimental investigations have been conducted. The surrogate method (SM) [133, 134], which was first introduced in the 1970s for the extraction of neutron-induced fission cross sections, was recently used to determine (n,γ) reaction cross sections. Based on the Weisskopf–Ewing limit of Hauser–Feshbach theory [135], which assumes that the decay probability of a compound nucleus (CN) is independent of its spin-parity, the method makes use of a surrogate reaction with an available beam and target to produce the same CN as the neutron-capture process. The cross section of the (n,γ) reaction is then indirectly determined by multiplying the calculated CN formation cross section by the measured γ decay probability.

The SRM is a variation of the SM. In this method, two surrogate reactions are employed to obtain the relative γ-decay probability ratio. With an available A1(n,γ)B1 reaction cross section as the reference, the A2(n,γ)B2 reaction cross section can be obtained by multiplying the reference reaction cross section by the measured ratio: $\frac{{\sigma }_{\text{A}1\left(n\mathrm{,}\gamma \right)\text{B}1}\left(E_{\text{n}}\right)}{{\sigma }_{\text{A}2\left(n\mathrm{,}\gamma \right)\text{B}2}\left(E_{\text{n}}\right)}\approx C_{\text{nor}}\frac{N_{\text{B}{1}^{*}\gamma }\left(E_{\text{n}}\right)}{N_{\text{B}{2}^{*}\gamma }\left(E_{\text{n}}\right)}$ (1) C_nor is the normalization factor defined by experimental conditions, including the target thickness, beam current, and detector efficiency. N_B*γ(En) is the number of CNs that decay into the g.s. by emitting γ-rays. Details can be found in [136]. The SRM has been successfully applied to determine the (n,f) cross sections [137-139], and a comprehensive review was recently published by Escher et al. [23]. In the case of (n,γ) reactions, theoretical studies [140, 141] indicate that the γ-decay probability is more sensitive to the spin-parity of CNs in the low-neutron-energy region. To apply the SRM to (n,γ) reactions, two-neutron transfer reactions (¹⁸O,¹⁶O) were employed to verify the SRM to determine the (n,γ) reaction cross section in the neutron-rich nuclei region. In this benchmark experiment, the ⁹¹Zr(n,γ)⁹²Zr and ⁹³Zr(n,γ)⁹⁴Zr reactions were chosen to check the SRM. In the measurements, the ⁹⁰Zr(¹⁸O,¹⁶O) and ⁹²Zr(¹⁸O,¹⁶O) reactions were used to produce the CNs ⁹²Zr* and ⁹⁴Zr*, instead of the (n,γ) reactions. The γ-rays emitted in the deexcitation of the CNs ⁹²Zr* and ⁹⁴Zr* were detected in coincidence with outgoing ¹⁶O particles to obtain the ratio. The indirectly determined ⁹³Zr(n,γ)⁹⁴Zr cross section with the SRM was then compared with the directly measured value [142].

The measurement was conducted at the Tandem-accelerator of the Japan Atomic Energy Agency (JAEA). An ¹⁸O beam with an energy of 117 MeV was bombarded on an isotopically enriched zirconium target, which was constructed in the form of self-supporting metallic foil. Downstream of the target, a silicon ΔE-E telescope was used to identify the light ejectile particles. Two LaBr₃(Ce) detectors were used for γ-ray detection. A faraday cup was installed to collect the ¹⁸O beam current for normalization purposes. After data analysis, the γ-decay probability ratios were obtained in a wide equivalent neutron energy range of 0–8 MeV with and. The ⁹³Zr(n,γ)⁹⁴Zr reaction cross sections were then determined relative to the cross sections of the ⁹¹Zr(n,γ)⁹²Zr reaction together with the deduced γ-decay probability ratios, as shown in Fig. 14.

Fig. 14Full-screen View

(Color online) Cross section of ⁹³Zr(n,γ)⁹⁴Zr. The red squares are the directly measured data, the open triangles are data deduced by the γ-decay probability ratio and ⁹¹Zr(n,γ)⁹²Zr cross sections, the blue triangles are data deduced by the γ-decay probability ratios and ⁹¹Zr(n,γ)⁹²Zr ENDF/B-VII.1 cross section, and the solid curve is the results calculated using the UNF code after constraining the parameters via experimental data [142]

The deduced ⁹³Zr(n,γ)⁹⁴Zr reaction cross sections were found to be lower than the ENDF/B-VII.1 data at E_n = 1–3 MeV, whereas at E_n < 1 MeV and E_n > 3 MeV, the deduced cross sections agreed well with the directly measured and ENDF/B-VII.1 data. Although the absolute SM may suffer from the spin-parity sensitivity problem in the low-neutron-energy region, the data imply that the sensitivity of the γ-decay probability ratio to the CN spin-parity distribution is partially reduced in the SRM. Furthermore, the SRM data can be used to provide a restriction of the model parameters in theoretical calculation in the relatively high-neutron-energy region, which in turn provides a reasonable estimation of the (n,γ) cross sections in the low-energy region.

After validating the SRM in the determination of the (n,γ) cross section, the neutron-capture cross sections of the unstable nuclei ⁹⁵Zr and ⁵⁹Fe were measured indirectly.

Zirconium is a typical s-process element belonging to the first s-process peak and is mostly produced by the main component in AGB stars. Its isotopic abundances are sensitive to both neutron exposure and neutron density and thus critical to constrain the s-process in AGB stars [143]. The most neutron-rich stable Zr isotope, ⁹⁶Zr, is highly sensitive to neutron density during the s-process because its production depends on the activation of the branching point at ⁹⁵Zr (with a half-life of 64 d) for neutron densities above approximately 10¹⁰ cm^-3. However, although the neutron cross sections of stable Zr isotopes have been carefully studied, the cross section of the ⁹⁵Zr(n,γ)⁹⁶Zr reaction remains highly uncertain. Therefore, the SRM can be used to determine the ⁹⁵Zr(n,γ)⁹⁶Zr cross section indirectly. A measurement was conducted at the JAEA with a similar experimental setup, details of which can be found in [142]. In this measurement, the ⁹⁴Zr(¹⁸O, ¹⁶O)⁹⁶Zr^* and ⁹⁰Zr(¹⁸O, ¹⁶O)⁹²Zr^* reactions were used to form the CNs ⁹⁶Zr^* and ⁹²Zr^*, respectively. When and were obtained from experiments, the cross sections of ⁹⁵Zr(n,γ)⁹⁶Zr could be determined via the ⁹¹Zr(n,γ)⁹²Zr cross sections and experimental ratios. The determined cross sections of ⁹⁵Zr(n,γ)⁹⁶Zr are shown in Fig. 15.

Fig. 15Full-screen View

(Color online) Cross section of ⁹⁵Zr(n,γ)⁹⁶Zr. The open triangles are deduced by multiplying our γ-decay probability ratio by the directly measured ⁹¹Zr(n,γ)⁹²Zr cross section, and the blue triangles are deduced by multiplying our γ-decay probability ratios with the ENDF data for the ⁹¹Zr(n,γ)⁹²Zr cross section. The blue curve is the theoretical calculation of the UNF code with parameters constrained by the experimental data in the high-energy region, and the red band is the uncertainties of the calculation results of the TALYS code with five sets of parameters constrained by the experimental data in the high-energy region [142]

The radioactive isotope ⁶⁰Fe with a half-life of ∼2.6 million years has been of great interest to the nuclear astrophysics community for several decades. The presence of ⁶⁰Fe in the interstellar medium of our Galaxy was confirmed through the detection of 1173- and 1332-keV γ-rays from the decay of its daughter ⁶⁰Co (t_1/2 = 5.27 yr) by the RHESSI and INTEGRAL satellites. Because the half-life of ⁶⁰Fe is considerably shorter than the age of the Galaxy, the observations provide strong evidence of ongoing stellar nucleosynthesis. ⁶⁰Fe has also been observed in deep ocean ferromanganese crusts, nodules, sediments, snow from Antarctica [144-149], and even lunar regolith [150], which indicates the occurrence of more than one nearby supernova event within several 10⁶ years.

To elucidate the production of ⁶⁰Fe in massive stars, a clear understanding of the ⁵⁹Fe(n,γ)⁶⁰Fe reaction is necessary. Based on the SRM, we measured the γ-decay probability ratios of the CNs ⁶⁰Fe^* and ⁵⁸Fe^*, which were populated by the two-neutron transfer reactions of ⁵⁸Fe(¹⁸O,¹⁶O) and ⁵⁶Fe(¹⁸O,¹⁶O). Subsequently, the ⁵⁹Fe(n,γ)⁶⁰Fe cross sections were determined using the measured ratios and directly measured ⁵⁷Fe(n,γ)⁵⁸Fe cross sections. The determined cross sections of ⁵⁹Fe(n,γ)⁶⁰Fe are shown in Fig. 16, and further details can be found in [151].

Fig. 16Full-screen View

Variation in the cross section of ⁵⁹Fe(n,γ)⁶⁰Fe as a function of equivalent neutron energy. The circles are obtained by multiplying the experimental γ-decay probability ratio by the directly measured ⁵⁷Fe(n,γ)⁵⁸Fe cross section. The dashed and solid curves represent the calculated results according to UNF and TALYS codes, respectively, with their parameters constrained by the γ-decay probability ratios of CN ⁶⁰Fe^* and ⁵⁸Fe^* in the high-energy region [151]

Indirect measurement of the ²⁵Mg(p,γ)²⁶Al reaction with the ANC method

²⁵Mg(p,γ)²⁶Al is the most important reaction during the Mg–Al cycle in the H-burning regions of stars. Its cross sections at stellar energies are essential to understanding the issues of radioactive ²⁶Al in the Galaxy and meteorites [98, 99]. The 57.7-keV resonance dominates the ²⁵Mg(p,γ)²⁶Al astrophysical reaction rates at relatively low temperatures; however, measuring its resonance strength directly can be challenging, and indirect measurement results deviate by a factor of approximately 2 [152-154].

A ²⁵Mg(⁷Li,⁶He)²⁶Al experiment was conducted using the Q3D magnetic spectrometer [119] with a 31.5-MeV ⁷Li beam from the CIAE HI-13 tandem accelerator. The angular distribution of the ²⁵Mg(⁷Li,⁶He)²⁶Al^6.364 reaction was measured as the first objective in this experiment. Moreover, the transfer reactions leading to the g.s. and first ten excited states were measured deduce the direct capture component of ²⁵Mg(p,γ)²⁶Al and verify the SF proportions for different angular momentum components calculated from the shell model (Fig. 17). To extract the optical potential of the entrance channel, the angular distribution of ⁷Li elastic scattering on ²⁵Mg was also measured [155].

Fig. 17Full-screen View

Measured angular distributions of the ²⁵Mg(⁷Li,⁶He)²⁶Al transfer reactions together with the DWBA calculations [155]

The proton SFs of ²⁶Al were analyzed with the shell model code NUSHELL using usdbpn Hamiltonian [156] in the sdpn model space, and the calculated ratios of the 2s_1/2, 1d_3/2, and 1d_5/2 orbits were adopted in the DWBA analysis. The angular distributions of the ²⁵Mg(⁷Li,⁶He)²⁶Al transfer reaction leading to 12 states in ²⁶Al were well reproduced with Jπ from 0⁺ to 5⁺ and the varied proportion of 2s_1/2, 1d_3/2, and 1d_5/2 components. Subsequently, the proton SFs of the 6.364-MeV state in ²⁶Al were derived to be 0.082±0.012, 0.162±0.024, and 0.028±0.004 for the 2s_1/2, 1d_3/2, and 1d_5/2 orbits, respectively. The present SFs are in agreement with the reanalysis results of three (³He,d) reactions [152-154].

Based on these SFs, the proton width and resonant strength of the 57.7-keV resonance in the ²⁵Mg(⁷Li,⁶He)²⁶Al reaction were deduced, and the astrophysical ²⁵Mg(⁷Li,⁶He)²⁶Al reaction rates were updated. The present results provide independent examinations of the ²⁶Al^6.364 proton SFs and 57.7-keV resonance strength. The ²⁵Mg(⁷Li,⁶He)²⁶Al reaction rates increased by approximately 5% at T 0.1 GK, and the uncertainties were significantly reduced.

Novel thick-target inverse kinematics method for the astrophysical ¹²C+¹²C fusion reaction

¹²C+¹²C fusion reactions play a crucial role in stellar evolution and explosive phenomena within the Universe [55, 157, 158], particularly during the final stage of massive star evolution, Type Ia supernovae (SNe Ia) events [159], and superbursts [160, 161]. The temperatures and densities [162] required for the ignition of carbon burning in massive stars and the superburst ignition depth in accreting neutron stars strongly depend on the ¹²C+¹²C reaction rate, which still remains elusive, to reconcile observations with theoretical models [163]. The Gamow peak of these reactions is 1.5 MeV at a temperature of 0.5 GK, which is far below the Coulomb barrier height of the ¹²C+¹²C system, at around 7.5 MeV. Thus, the cross section decreases rapidly in the energy region of interest and is yet to be reported from direct measurements below 2.1 MeV [164-172].

A series of direct measurement data suggest the existence of sub-barrier resonances in the ¹²C+¹²C fusion reaction [168-170], leading to significantly enhanced reaction rates compared with the standard non-resonance rate given by Caughlan et al. [173, 174]. Owing to the presence of potential resonances in the unmeasured energy ranges, it is extremely difficult to provide an extrapolation to the lower energies, including the Gamow energy region for the ¹²C+¹²C fusion reaction. Therefore, determining the resonance parameters of proton and α decaying channels is extremely important in the Gamow energy region.

A thick-target inverse kinematics (TTIK) measurement was conducted for ²³Na+p [114, 175] at the CIAE HI-13 tandem accelerator. The experiment set up is shown in Fig. 18. A ²³Na beam with an energy of 110 MeV was delivered and directed onto a self-supporting ${\left({\text{CH}}_{\text{2}}\right)}_{{}_{\text{n}}}$ target. A thick carbon target was used to measure the background. For the measurement of the excitation functions, the particles emitted in the ²³Na+p and ²⁰Ne+α exit channels were detected with a silicon telescope system at 0° along the beamline. The silicon telescope system consisted of a 70-μm double-sided silicon strip detector (DSSD), 1.5-mm multi-guard silicon quadrant (MSQ), and 1-mm MSQ. Six three-inch LaBr₃ detectors were uniformly arranged around the target chamber to measure the characteristic γ rays from the residual nuclei ²³Na and ²⁰Ne.

Fig. 18Full-screen View

Setup of the ²³Na+p thick-target experiment [114]

In the relevant energy range, the exit channels of compound ²⁴Mg consisted of p₀, p₁, α₀, and α₁. For the residual nuclei ²³Na and ²⁰Ne, the full-energy peak efficiencies at characteristic energies of 440 keV and 1634 keV were 28.2 % and 12.6 %, respectively.

The energy spectrum of charged particles obtained by silicon detectors contains a series of excitation function effects. Through the data analysis process, including γ-charged-particle coincidence, two-body reaction kinematics reconstruction, and carbon background deduction, the excitation functions of the CN ²⁴Mg populated by the ²³Na+p entrance channel were obtained, as shown in Fig. 19. R-matrix analysis was performed to extract a series of exit channel resonance parameters. Nearly fifty ²⁴Mg resonances were introduced to reproduce the excitation functions, including those most relevant to the ¹²C+¹²C fusion reaction. The branching ratios and astrophysical S-factors of different decay channels were evaluated with the theoretically calculated reduced width of the ¹²C+¹²C entrance channel. Our analysis revealed that the sharp increase in the astrophysical S-factor reported by Tumino et al. disappeared, which is consistent with the results from antisymmetrized molecular dynamics calculations [176].

Fig. 19Full-screen View

Excitation functions for the proton and α exit channels. p₀, p₁, and α₀, α₁ represent ¹H(²³Na, p₀)²³Na, ¹H(²³Na, p₁)²³Na, and ¹H(²³Na, α₀)²⁰Ne, ¹H(²³Na, α₁)²⁰Ne, respectively. The error bars primarily account for accidental coincidence errors, statistical uncertainties, carbon background, and p₁(α₁) errors in the p₀(α₀) calculation. See [114] for details

Direct calibration of neutron detectors for laser-driven nuclear reaction experiments

In nuclear physics experiments with laser-induced plasma, quantitatively measuring the reaction products is highly challenging because of the interference of electromagnetic pulses (EMP) induced by high-intensity lasers. Fast scintillation detectors with time-of-flight (TOF) detection are widely chosen for fast neutrons [182-184]. The calibration of neutron detectors is crucial for measuring the yield of neutron products. However, energy calibration methods for detection systems aimed at laser-induced plasma environments have not yet been systematically demonstrated.

In a previous study [185], we developed a direct calibration method with a gated fission neutron source ²⁵²Cf to solve this problem. This study demonstrated that the gated fission neutron source approach, with an unique “window” function, exhibited the highest background-γ-rejection. It also improved upon the confidence level of the final results of both liquid and plastic scintillators obtained from the Compton edge and neutron beam methods.

The gated fission neutron source approach is a direct experimental calibration method. The experimental setup of the gated calibration with a fission neutron source can be found in [185], where a ²⁵²Cf source with a neutron activity of 10² Bq was used. Its spontaneous fission neutron spectrum was determined as the standard neutron spectrum by International Atomic Energy Agency (IAEA) [186], which is typically used to calibrate the efficiency of neutron detectors [187, 188]. For each fission, on average, 3.6 neutrons are emitted from ²⁵²Cf, and around 9.3 gammas are simultaneously emitted from the rapid decay of the fission fragments [189]. Thus, one can construct the TOF between the neutrons and prompt gamma. Therefore, both the companion gamma signals (recorded by the plastic EJ200 scintillator) and neutron signals (recorded by the scintillation detector to be calibrated) were used as the triggers to open the AND logic gate to start the recording process of the digitizer DT5730SB. To analyze the AND gate, the interval between the prompt gamma and one neutron signal was adjusted appropriately according to the neutron energy to reduce background interference. For the calibration of 2.45-MeV neutrons, the time interval was set as 120 ns, whereas the recording period was set as 600 ns. After the AND gate was opened, the waveforms of the neutron signals from the to-be-calibrated neutron detectors were recorded by the digitizer, as shown in Fig. 20.

Fig. 20Full-screen View

(Color online) Two-dimensional spectrum of the PSD vs. TOF for neutron signal calibration [185]

As shown in Fig. 20, the background interference in the calibration experiment was significantly reduced because the gamma signals recorded by the EJ200 and the neutron signals were simultaneously used to determine whether to open the AND gate to start recording the signals. Furthermore, because the scintillator has different responses to a neutron or a gamma photon, they could be checked by analyzing the waveforms recorded by DT5730SB. Moreover, we distinguished the neutron signal from spurious gamma backgrounds with both the PSD and TOF functions simultaneously; hence, the background could be further reduced by using the pulse shape discrimination [190, 191] and TOF methods. Thus, the purity of neutron signals was significantly improved.

For comparison, we used two other popular methods to calibrate the neutron detectors. First, a direct calibration method was performed with the 2.45-MeV neutrons produced from the D(d, n)³He reaction using the Cockcroft–Walton accelerator at the CIAE [192]. Second, an indirect calibration method commonly used with a Compton edge [193-195] was conducted. The comparison results for the three methods is shown in Table 4.

In conclusion, the gated fission neutron source method can directly produce the experimental calibration results of neutron yields from laser-driven nuclear reactions. It exhibits a higher background-γ-rejection rate, which improves the confidence level of the final results. Furthermore, with a more active ²⁵²Cf fission source and optimized setup (longer distance, narrower gating, etc.), the calibration time may be shortened, and a more extensive energy range of neutrons and a smaller uncertainty can be achieved. Consequently, neutron yields from nuclear reactions in laser-induced plasma may be obtained more precisely. This method can provide an effective and straightforward calibration system for neutron detectors for future laser-driven nuclear fusions and laser-induced neutron sources.

Deuterium–deuterium fusion in nanowire plasma driven by a nanosecond high-energy laser

It is well known that in nuclear astrophysics, especially in the Gamow window, the energies of the ions of interest range from a few keV to hundreds of keV. Therefore, the interaction of nanosecond (ns) lasers with solid targets is well suited to generating extreme plasma environments in the above energy range. A previous study [196] found that, in nanowire form, nanostructures on the surface of the target could absorb laser energy with high efficiency. The nanowire target can generate an extreme plasma environment an order of magnitude higher in temperature and density than a planar target, and theoretical calculations indicate that the neutron yield is expected to be improved when a ns laser interacts with nanowire targets. However, the effect of the interaction between kJ-level ns lasers and nanowire targets on energy absorption and neutron yield is still unclear. In this study, based on the collision of two plasma streams, we first conducted an experimental study on kJ-level ns laser irradiation of a CD₂ nanowire target using the colliding plasmas method [197, 198] and evaluated the energy conversion efficiency between them by measuring the yield of nuclear reaction products.

The experiment [199] was performed at the ShenGuang II laser facility of the National Laboratory on High Power Lasers and Physics in Shanghai, China. Figure 21 shows a schematic diagram of the experimental setup with the target layer changed from LiD to CD₂ [200-202]. There were eight laser beams aimed at the center of the target chamber, and each beam could deliver an energy of approximately 250J with a pulse width of 1ns at a wavelength of 351nm (3ω). A dual target was located at the center of the chamber. Both of the targets had 2.0 mm × 2.0 mm sized copper bases, which were coated with 200-500 μm-thick deuterated hydrocarbon (CD_1.96H_0.04)_n layers. The opposing layers on the target were separated by 4 mm. The ns lasers were arranged as two sets (4 + 4), and each set had four lasers focusing on one side of the dual target. The diameter of the focal spots was approximately 150 μm, and the corresponding intensity was approximately 6 × 10¹⁵ W/cm². A TOF detection system was used with scintillation detectors and oscilloscopes to record the neutrons arriving at the detectors simultaneously and avoid the strong EMP impact on shooting time. The interaction between the counter-streaming plasma flows was measured with optical diagnostics, including Nomarski interferometry and shadow graphics, using a 9th probe laser with a duration of 70 ps and wavelength of 526 nm. The probe laser was passed through the plasma interaction zone generated by the main laser beams to achieve interference images. Meanwhile, snapshots of the plasma at different times were taken by changing the delay time between the probe and main lasers. Using the Abel inversion approach [203] for the interference data, the plasma density distribution was obtained.

Fig. 21Full-screen View

(Color online) Schematic layout of the experimental setup. The materials of the main targets are lithium deuteride (LiD) with density ρ_LiD = 0.906 g/cm³ (see the enlarged illustration in the upper right corner). The counter-streaming plasmas are produced from the main targets via ablation with 4 laser beamlines. A lead-shielded plastic scintillator detector is used to record the neutron products. The interference images are taken by a Nomarski interferometer [204]

The developed numerical calculation results indicated that as E_cm increased, the cross section increased, whereas the number of ions (N) increased and then decreased. Thus, as shown by the solid blue line in Fig. 22, the majority of the neutron yields originated from the E_cm energy range 10–30 keV. The neutron data from the EJ301 and BC420 detectors were calibrated using the gated fission neutron source ²⁵²Cf method [185]. The neutron yields for various target specifications are displayed in Fig. 23 at the same order of 10⁶ per shot. The systematic uncertainty was 47% for EJ301 and 51% for BC420.

Fig. 22Full-screen View

Neutron yield contributed by deuterium ions with different E_cm energies. Three data lines are shown in this chart: the number of the ions from the experimental diagnostic (dotted green line), D(d,n)³He cross section (dashed red line), and calculated neutron yield (solid blue line) [199]

Fig. 23Full-screen View

(Color online) Neutron yields with statistical uncertainties from EJ301 and BC420 detection and different target parameters. The circles represent the results of EJ301 detection and the squares represent those of BC420. The black diamond represents the results of the numerical calculation with the optical diagnostics approach for the 2nd shot run. Different colors correspond to different target parameters [199]

The results indicate that the nanowire target could not significantly enhance the energy absorption of the ns laser, even with high energy, compared with the results of the planar target. This conclusion was supported by the experimental results, numerical calculation, and magneto-hydrodynamic simulation. Moreover, this study provides a useful experimental method for investigating nuclear reactions in a plasma environment with an energy region of interest of tens of keV in nuclear astrophysics.

Measurement of the ⁷Li(d,n)⁸Be astrophysical S-factor in laser-induced full plasma

Plasma is known as the fourth state in the universe and is composed of many ions, electrons, and other particles. In the process of laser-driven jet collision interactions, there are various instabilities, such as two-stream instability and Weibel instability, which may generate electromagnetic fields. In addition, there are also uncertainties in the energy and focal spot of each laser shot, which pose significant challenges in measuring the nuclear reaction during the experimental process. Using the collision method of two plasma jets, experimental research on the fusion reaction of ⁷Li(d,n)⁸Be in a plasma environment was conducted at the Shenguang-II laser facility, the National Laboratory on High Power Lasers and Physics, Shanghai, China. The experimental setup is schematically shown in Fig. 21. We established the theoretical model and numerical simulation method for studying the plasma collision process of the deuterium–lithium fusion reaction. We proposed an innovative method, namely, the Self-Calibration Method for Nuclear Reactions in Plasma (SCM-NRP), to eliminate the influence of plasma and laser parameter instability on experimental measurements. For the first time, we measured the astrophysical S-factor in plasma and obtained S=(24±8) in the Gamow window around 173 keV, as shown in Fig. 24 [204]. We experimentally demonstrated that the plasma effect may not have a significant impact on the ⁷Li consuming reaction related to the Big Bang lithium abundance puzzle near 173 keV. This study provides theoretical and experimental methods and data support for the development and application of research related to laser plasma and laser nuclear physics in the fields of fundamental nuclear physics and high-energy-density physics, promoting the development and cross integration of disciplines.

Fig. 24Full-screen View

(Color online) Comparison of the ⁷Li(d,n)⁸Be reaction astrophysical S-factors in full plasma (our study) and non-plasma environments (all other studies) [204]

Effect of metallicity on SNe Ia luminosity

Normal SNe Ia can serve as a cosmological standard candle to measure galactic distances, which can reveal cosmic motion and compositions when combined with cosmological models [205-207]. In fact, the light of an SNe Ia explosion originates from the decay of synthesized radioisotopes, and the peak luminosity is dominated by the amount of ⁵⁶Ni formed during the nucleosynthesis [208]. However, the ⁵⁶Ni yield is closely related to the initial metallicity of the SNe Ia progenitor (Z_pro) [209, 210]. It is well known that main-sequence stars inherit the metal elements produced by previous stars from the ambient interstellar medium during their formation. Therefore, the initial metallicity of the SNe Ia progenitor should increase with the accumulation of heavy elements in the Universe, which would have an important effect on the synthesis of ⁵⁶Ni. A varying “standard candle” may then lead to misconceptions about the origin and evolution of the Universe.

Now, it is widely accepted that SNe Ia are produced by the thermonuclear explosion of a carbon-oxygen (CO) white dwarf in a binary system, whereas our understanding of the progenitor system, accretion rate, and explosion mechanism is still unclear [211-214]. Both near-Chandrasekhar mass (near-M_ch) and sub-Chandrasekhar mass (sub-M_ch) models are promising progenitor scenarios for SNe Ia. By analyzing the 1D, 2D, and 3D simulation results, we found that the ⁵⁶Ni yield depends linearly on Z_pro, $M\left({}^{56}\text{Ni}\right)\propto 1-b\left(Z_{\text{pro}}/Z_{\odot }\right),$ (2) where Z_⊙ denotes the solar metallicity, and the slope b is approximately 0.050 and 0.078 for the sub-M_ch and near-M_ch models, respectively [215]. This suggests that the peak luminosity of the near-M_ch SNe Ia is more influenced by the initial metallicity of the progenitor than that of sub-M_ch SNe Ia.

It is difficult to measure the initial metallicity of SNe Ia progenitors either from the supernova remnants or their environments [216-220]. However, studies on cosmic mean metallicity (CMM) provide a possibility of estimating Z_pro. Because the initial metal elements of the progenitors are inherited from their ambient interstellar medium, it is reasonable to consider that Z_pro roughly follows the CMM evolution. Many studies on CMM evolution have shown or implied that log₁₀(Z_CMM/Z_⊙) is approximately linear with redshift, at least in the range of z<5 [221-224]. ${\log }_{10}\left(Z_{\text{CMM}}/Z_{\odot }\right)=-az+a_0,$ (3) where a indicates the evolution rates of the CMM, which are approximately 0.22 and 0.15 according to the quasar absorption-line systems (QASs) and cosmic star formation rates (CSFRs). The QASs suggest a faster evolution rate of the CMM than the CSFRs.

After combining the two relationships, it is clear that the yield of the synthesized ⁵⁶Ni decreases with the cosmological chemical evolution, which indicates that the previous SNe Ia is brighter than the present when at the same distance. The relationship between distance modulus μ and luminosity distance dL is corrected to $\mu =5\log \left[d_{\text{L}}{\left(\frac{1-b\times {10}^{az}}{1-b}\right)}^{\frac{1}{2}}\right]-5,$ (4) where the solar metallicity is taken as the current CMM, that is, a₀=0. The luminosity distance can be further expressed as a function of redshift z and the current proportion of dark energy Ω_Λ based on the Λ cold dark matter (ΛCDM) model, $d_{\text{L}}=\frac{1+z}{H_0}{{\displaystyle {\int }_0^z\left[\left(1-{\text{Ω}}_{\text{Λ}}\right){\left(1+z^{\prime }\right)}^3+{\text{Ω}}_{\text{Λ}}\right]}}^{\frac{1}{2}}\text{d}{z}^{\prime },$ (5) where H₀ is the Hubble constant. Subsequently, Ω_Λ can be deduced using the measurements of the distance modulus μ and redshift z of the SNe Ia. The cosmic age can also be estimated using the following equation: $t_0=\frac{2}{3H_0\sqrt{{\text{Ω}}_{\text{Λ}}}}\ln \left(\frac{1+\sqrt{{\text{Ω}}_{\text{Λ}}}}{\sqrt{1-{\text{Ω}}_{\text{Λ}}}}\right).$ (6) Finally, the corrected dark energy proportions would be higher than the Planck results, and the Universe would be 0.2–0.4 billion years older than the previously estimated value (shown in Fig. 25) [215]. By studying the effect of metallicity on the SNe Ia luminosity, a more accurate distance scale can be obtained. The accurate measurement of intergalactic distances may clarify several major puzzles in current cosmology, including the Hubble tension, formation of the cosmic structures, and evolution of dark energy [225].

Fig. 25Full-screen View

(Color online) Dark energy proportions (Ω_Λ) and cosmic ages predicted using Planck measurements (gray columns), the sub-M_ch model (orange columns), and the near-M_ch model (green columns) with faster and slower CMM evolutions [215]

Neutrino nucleosynthesis in core-collapse supernovae

Massive stars typically undergo H, He, C, Ne, O, and Si burning and end up with iron-peak elements. When the mass of the iron core exceeds the effective Chandrasekhar mass, the core starts to collapse and a neutron star or a BH is formed. The gravitational binding energy of the proto-neutron star, E_total× 10⁵³ erg, is removed by a powerful stream of neutrinos during the cooling stage, which may have important implications for nucleosynthesis.

The total energy is approximately equally distributed among all six neutrino species, v_e, ${\overline{v}}_e$, v_μ, ${\overline{v}}_{\mu }$, v_τ, and ${\overline{v}}_{\tau }$ and the neutrino emission shows an exponentially decreasing luminosity $L=L_0{e}^{-t/{\tau }_v}$ with the characteristic time τν=3 s [226]. Assume that the initial radius of the shell in which the seed nucleus resides is r₀, and the average shock velocity interior to r₀ is v_sh. Before the arrival of the shock wave, the state of the shell remains almost unchanged. The radius is a constant, r(t<t₀)=r₀, and the temperature is approximately equal to the temperature of hydrostatic burning. When the shock wave arrives, the temperature increases instantaneously to a peak value [226], $T_{\text{peak}}=2.4{\left(\frac{E_{\text{expl}}}{{10}^{51}\text{ erg}}\right)}^{1/4}{\left(\frac{r_0}{{10}^9\text{ cm}}\right)}^{3/4}\text{ GK,}$ (7) where E_expl～ 1.2×10⁵¹ ergs is the total kinetic energy of the shock. Then, the overpressure drives rapid expansion. The expansion of the shocked mass element is approximately adiabatic, and its temperature decreases exponentially with the hydrodynamic time scale τ_HD [226], $T\left(t\right)=T_{\text{peak}}{e}^{-\left(t-t_0\right)/3{\tau }_{\text{HD}}},$ (8) where τ_HD≈446ρ^-1/2 s, and ρ in units of g/cm³ is the mean density within the radius r₀ (that is, r<r₀). The shocked material in the outer layer of the star is assumed to be moving at a typical constant speed v_p in the expansion phase. Therefore, the neutrino flux is [226] ${\varphi }_v\left(t\right)=｛\begin{array}{cc}{\varphi }_{v,0}{e}^{-t/{\tau }_v}& t<t_0,\\ {\varphi }_{v,0}{e}^{-t/{\tau }_v}{\left[1+\left(t-t_0\right)/{\tau }_{\text{p}}\right]}^{-2}& t>t_0,\end{array}$ (9) where ${\varphi }_{v,0}=\frac{E_{\text{total}}{\tau }_v^{-1}}{4\pi r_0^2{n}_{\text{f}}\langle E_v\left(T_v\right)\rangle },$ (10) where n_f=6 is the number of neutrino species, and $\langle E_v\left(T_v\right)\rangle$ is the average energy of the neutrinos.

For the v_e-process (Z, A)+v_e→(Z+1, A)+e^-, the abundance ratio of the daughter nucleus to parent nucleus satisfies the differential equation $\dot{\mathcal{R}}\left(T_v,t\right)={\varphi }_v\left(t\right)\langle {\sigma }_v\left(T_v\right)\rangle -\left[{\lambda }_{\beta }\left(T\right)+{\lambda }_{\gamma }\left(T\right)\right]\mathcal{R}\left(T_v,t\right),$ (11) where the first term on the right side denotes the production rate of the daughter nucleus via the ν_e-process, whereas the second term denotes the destruction rate via β^± decay and photodisintegration. The expression for the ν_e-nucleus cross section for a specific nucleon state X has the following form [227]: ${\sigma }_X\left(E_v\right)=\frac{G_F^2{\cos }^2{\theta }_{\text{C}}}{\text{π}}{g}_{\text{V/A}}^{2}B\left(F/GT\right)p_{\text{e}}{E}_{\text{e}}F\left(Z_{\text{f}},E_{\text{e}}\right),$ (12) where G_F is the Fermi constant, θ_C is the Cabibbo angle, g_V and g_A are the vector and axial-vector interaction constants, respectively, B(F/GT) is the square of the Fermi/Gamov–Teller nuclear matrix element for transition to a certain state of the final nucleus, divided by (2Ji+1), Eν is the energy of the incoming neutrino, and E_e and p_e are the energy and momentum of the outgoing electron, respectively. The Fermi function F(Z_f, E_e) contains a Coulomb correction of the lepton and the daughter nucleus in the final state. The quantity entered into the calculations is the total cross section [228], $\langle {\sigma }_v\left(T_v\right)\rangle ={\displaystyle \sum _X{\displaystyle {\int }_{E_{\text{th}}}^{\infty }\text{Φ}\left(E_v,T_v\right)}}{\sigma }_X\left(E_v\right),\text{d}{E}_v,$ (13) where E_th is the threshold energy of the reaction. $\text{Φ}\left(E_v,T_v\right)$ is the neutrino spectrum, which is assumed to follow a Fermi–Dirac distribution with a vanishing chemical potential [226, 228, 229].

We considered the effects of neutrino temperature and shock velocity at different shell radii, and the maximum yields of ²⁶Al and ⁷⁴Se were found at r₀=11000 and 8000 km, respectively (shown in Fig. 26 and 27, respectively) [230, 231]. After considering the Galactic mass distribution, we estimated that the total mass of ²⁶Al produced via the νe-process was 0.16±0.08 M_⊙ by taking solar metallicity as representative (marked as Z_⊙) and 0.23±0.13 M_⊙ by using the Galactic metallicity distribution (marked as Z(rG)) (shown in Fig. 28) [230]. The νe-process could contribute 10% of the ²⁶Al mass estimated from the γ-ray observation [232]. These results are consistent with those of previous studies, which suggested that approximately 0.2 M_⊙ of ²⁶Al is contributed by the neutrino process [229, 232]. Furthermore, it is worth emphasizing that this semi-analytic approach allows us to deviate from the extremely time-consuming numerical simulations and carefully study the influences of several important factors, such as shell radius, shock velocity, neutrino spectrum, Galactic mass, and metallicity distribution. We conclude that the biggest uncertainty originates from the neutrino spectrum, while the second-most important uncertainties arise from the initial mass function of stars and the core-collapse supernovae formation rate [230]. Therefore, these studies facilitate an intuitive understanding of the buried implicit assumptions in previous studies.

Fig. 26Full-screen View

(Color online) Abundance ratios of ²⁶Al and ²⁶Mg in the process for different radii of the O/Ne shell and shock velocities with a neutrino temperature of 2.8 MeV [230]

Fig. 27Full-screen View

(Color online) Abundance ratios of ⁷⁴Se and ⁷⁴Ge in the process varying with the shell radius for different neutrino temperatures [231]

Fig. 28Full-screen View

(Color online) Probability density distributions of the total mass of ²⁶Al produced by the ν_e-process in the Galaxy (including the maximal effects of neutrino flavor oscillations) [230]

JUNA Run-2 plan and upgrade

JUNA Run-1 experiments have demonstrated a promising outlook for accurately measuring nuclear astrophysical reactions in underground laboratories. There are still many reactions worth studying in/near the Gamow energy region. In JUNA Run-2, we aim to utilize additional accelerator beam time with higher beam intensities (≥ 1 emA), more radiation-resistant targets, such as diamond targets, and more efficient detection arrays to push the current measurement to lower energy regions and cover a wider Gamow window. The largest improvement over Run-1 is the use of a windowless gas target, which allows us to choose isotope-enriched gas such as ³He and ²²Ne as targets. Once the JUNA experiments resume in 2025, a plan will be carried out, involving three types of nuclear astrophysics experiments.

The first type will push the holy grail and neutron source reactions to lower energies based on the Run-1 experiments, bringing them closer to the Gamow window.

The second type involves new neutron source reaction and neutrino production reaction measurements, which will use a newly developed windowless gas target that has already been tested on the ground and in accelerator experiments in 2024.

The third type involves other radioactive capture nuclear astrophysics reactions, most of which involve γ-ray measurements.

To perform the above tasks, the JUNA team has upgraded the BGO and ³He detectors, developed new materials such as diamonds for solid radiation-resistant targets, and completed ground accelerator experiment tests.

With the increasing number of experimental proposals and growing activity within the nuclear astrophysics community, it is increasingly challenging to achieve efficient experimental operations relying solely on the JUNA 400-kV accelerator. To fully exploit the benefits of the JUNA deep underground platform, after extensive discussions, the team has proposed a future accelerator plan known as Super-JUNA. The main features of this plan are as follows:

(1) The focus is on maintaining a leading position in at low energy and high current, ensuring the holy grail and neutron source reactions fully span the Gamow window.

(2) To ensure statistical accuracy at low energies and the connection with high-energy ground experiments, the accelerator will be designed with a strength of 20 mA and a maximum voltage of 800 kV.

(3) Considering the selection and technical basis of various accelerations, the accelerator will use an open high-voltage platform consistent with JUNA and reache the above indicators through an optimized ion-source and accelerator-tube design.

Super-JUNA is expected to start construction in 2026 and be put into operation in 2028. At that time, Run-3 experiments will be conducted based on JUNA and Run-4 experiments will be concurrently performed based on Super-JUNA. It is expected to achieve comprehensive coverage of important reactions on the “wish list” for direct measurement of deep underground nuclear astrophysics reactions. The establishment of the Super-JUNA platform will provide China with a comprehensive research capability in underground nuclear astrophysics. This platform will address a series of major scientific issues in nuclear astrophysics and become an important center for direct measurements and international collaboration in nuclear astrophysics.

The experimental plan of JUNA Run-2 is shown in Table 5, with the reaction, target, astrophysical environment, and energy range of interest parameters.

Direct/indirect experiments on ground accelerators

Researchers at the CIAE have conducted extensive indirect/direct experimental research on various ground accelerator facilities. These studies involved various processes in astrophysics, such as H burning, He burning, the s-process, r-process, and rp-process, and have provided important systematic reference data that will highlight the nature of stellar evolution. In the future, with an increase in international cooperation, more extensive research will be conducted on international platforms.

To extend nuclear astrophysics research, BRIF plans to expand further, which will include but not be limited to the following:

(1) Adding a collinear resonance ionization laser spectroscopy and decay measurement device to the ISOL system to measure decay properties for astrophysical r and rp processes.

(2) Expanding the tandem accelerator experimental system to accommodate unstable beam experiments, using a recoil mass spectrometer and superconducting solenoid, etc. to measure astrophysical reactions for rp- and r-processes.

Looking ahead, the CIAE will continue to realize the BISOL plan. BISOL will use a neutron driver, such as from an accelerator, to achieve fission ions with a ²³⁵U target. This acceleration of neutron-rich fission beams will provide opportunities for intense neutron-rich beams, which is crucial for conducting comprehensive studies of reactions and decays along the astrophysical r-process. There are many potential locations for BISOL; however, the most attractive is Huizhou, Guangdong. Here, CiADS, which can serve as a driver accelerator, and HIAF, which can serve as part of a post-accelerator, are currently under construction.

Laser-driven studies on nuclear astrophysics

In recent years, in laser-driven studies on nuclear astrophysics, we have conducted detector calibration for laser nuclear physics experiments. Based on laser facilities such as Shenguang-II, studies on deuterium–deuterium and deuterium–lithium fusion reactions in plasma environments have also been performed. During the research process, a high-efficiency calibration method for neutron detectors was proposed, and a theoretical model and numerical simulation method suitable for studying nuclear reactions in plasma environments through jet collisions were developed. For the first time, the astrophysical S-factor near 173 keV within the Gamow window in a plasma environment was experimentally obtained. The above results promote our understanding of the influence of plasma environments on nuclear reactions and the application of lasers in nuclear physics.

In subsequent research, it is necessary to optimize the quality and stability of beams generated by proton, neutron, and γ-ray lasers and improve the high-repetition rate of these lasers to provide a high-quality source for conducting nuclear reactions. In addition, developing new experimental methods to reduce the impact of strong electromagnetic interference on nuclear reaction parameter measurement is of vital significance. CIAE researchers will continue to develop nuclear radiation detectors suitable for strong electromagnetic environments, measure ⁶Li(d,n) nuclear reactions in plasma environments, and develop related theories and experimental methods.

Theoretical studies

Studies on supernova nucleosynthesis allow us to decode the evolution of the Universe and the origin of heavy elements from astronomical observations. We investigated the influence of the initial metallicity of the SNe Ia progenitor on the ⁵⁶Ni yield synthesized during explosions and found that the previous SNe Ia was brighter than the present when they were at the same distance, which would lead to inaccurate distance measurements in cosmology. In addition to this, other factors that may affect nucleosynthesis, such as the rotation of the progenitor and the explosion mechanism of SNe Ia, must also be carefully studied to ensure the accuracy of cosmological measurements, which are the basis for a correct understanding of cosmic evolution history.

In addition, we studied the influences of a powerful neutrino stream on the synthesis of ²⁶Al and ⁷⁴Se in core-collapse supernovae, which are helpful in exploring the origin of the Galactic ²⁶Al and the formation of the solar system. However, unraveling these mysteries requires more precise theoretical calculations of the synthesis of more nuclides. Furthermore, it requires further clarity on the mechanism of supernova explosions, and correct and precise astrophysical reaction rates are necessary as inputs to the nuclear reaction network [233].

In the future, CIAE researchers will improve the theory and calculation of the nucleosynthesis network and introduce processes such as neutrino physics and fluid dynamics to better explain astrophysical problems, such as the origin of heavy elements. The CIAE will also focus more on expanding the numerical simulation of the impact of reaction rates on the element abundance observation in stars.